Circle Length Calculator
Enter the radius, diameter or length (circumference) of a circle to convert between all three.
Updated
Circle Length Calculator
"Circle length" is another name for the circumference of a circle: the distance all the way around its edge. Our Circle Length Calculator converts freely between the radius, the diameter and the length, so whichever one you have, you get the other two, with the working, the exact answer in terms of π, the area and a drawing.
Quick answer
The length of a circle is 2 × π × radius: C = 2π × 5 cm ≈ 31.42 cm.
- From the diameter: C = π × d, so 10 cm gives ≈ 31.42 cm
- Radius from the length: r = C ÷ 2π, so 100 cm gives ≈ 15.92 cm
- Diameter from the length: d = C ÷ π
- Units: the length uses the same unit as the radius (cm stays cm)
What Is the Length of a Circle?
If you traced the edge of a circle with a piece of string and then pulled the string straight, its length would be the length of the circle, better known as the circumference (C). It depends only on the size of the circle: the radius r, from the centre to the edge, or the diameter d = 2r, right across through the centre.
Circle Length Formulas
Use the formula that matches what you know.
| You know | Formula |
|---|---|
| The radius | C = 2πr |
| The diameter | C = πd |
| The length | r = C ÷ 2π |
| The length | d = C ÷ π |
π (pi) is about 3.14159. It is the same for every circle, which is why one number is enough to find the other two.
Converting Between Radius, Diameter and Length
The three measurements sit in a chain. Double the radius to get the diameter, then multiply by π to get the length. To go back, divide by π and then by 2.
C ÷ π = d, d ÷ 2 = r
Why the Length Is π Times the Diameter
Roll a circle along a straight line for exactly one turn. However big the circle is, the distance covered is always about 3.14 times its diameter. That ratio is π, so C = πd, and since d = 2r, C = 2πr.
Circle Length Examples
| Known | Exact | Result |
|---|---|---|
| r = 5 cm | 10π | C ≈ 31.42 cm |
| d = 10 m | 10π | C ≈ 31.42 m |
| r = 2.5 in | 5π | C ≈ 15.71 in |
| d = 24 ft | 24π | C ≈ 75.40 ft |
| C = 100 cm | 50 ÷ π | r ≈ 15.92 cm |
Leaving π as a letter keeps the answer exact: a radius of 5 gives 10π. Multiply by 3.14159 only at the end, so rounding does not creep in.
Circle Length in Real Life
- Wheels: a wheel 0.7 m across moves π × 0.7 ≈ 2.199 m each turn, so 1,000 turns cover about 2.2 km.
- Trim and edging: a round table 1.2 m across needs about 3.77 m of edging.
- Measuring a tree or pipe: wrap a tape around it to get C, then d = C ÷ π gives the width you cannot measure directly.
- The Earth: the equator is about 40,075 km long, so the radius is about 40,075 ÷ 2π ≈ 6,378 km.
Common Mistakes
- Using πr²: that is the area. The length is 2πr.
- Mixing up r and d: 2πr and πd are equal. Using 2π with the diameter doubles the answer.
- Square units: a circle's length is a length (cm, m, ft), not an area (cm²).
- Rounding π too early: 3.14 instead of π gives 31.40 instead of 31.42 for r = 5.
- Dividing by π only: C ÷ π is the diameter. Halve it again for the radius.
Key Terms
- Circle length
- The distance around the circle, its circumference, C.
- Radius
- From the centre to the edge, r.
- Diameter
- Across the circle through the centre, d = 2r.
- Pi (π)
- Length ÷ diameter for every circle, about 3.14159.
How to Use the Circle Length Calculator
- Choose what you know. Pick Radius, Diameter or Circumference (the length of the circle).
- Enter the value. Type the number, such as 5, and pick a unit if you want one (mm, cm, m, km, in, ft, yd or mi). Decimals and fractions such as 3/4 work.
- Read and copy the result. The length (or, from a circumference, the radius) appears as you type, with the working, the exact answer in terms of π, the other measurements, the area and the result in other units. Press Copy to copy it, or Clear or Esc to start again.
Example: a tape around a tree trunk reads 1.5 m. Choose Circumference, enter 1.5 and pick m. The radius is about 0.2387 m and the diameter about 0.4775 m.
Who Can Use This Calculator?
Frequently Asked Questions (FAQs)
What is the length of a circle?
It is the circumference: the distance all the way around the edge. Find it with C = 2πr. A radius of 5 cm gives 10π ≈ 31.42 cm.
How do you find the length of a circle from the diameter?
Multiply the diameter by π: C = πd. A diameter of 10 cm gives 10π ≈ 31.42 cm.
How do you find the radius from the length of a circle?
Divide the length by 2π: r = C ÷ 2π. A length of 100 cm gives r ≈ 15.92 cm, and the diameter is C ÷ π ≈ 31.83 cm.
Is circle length the same as arc length?
Not quite. An arc is only part of the edge. The circle length is the whole edge, the arc for a full 360° turn. An arc of angle θ is θ ÷ 360 × 2πr long.
What unit is the length of a circle in?
The same unit as the radius or diameter. A radius in cm gives a length in cm, not cm², because it is a distance, not an area.
What is the length of a circle with a radius of 1?
2π, which is about 6.283. A circle with a diameter of 1 has a length of π, about 3.142.
Is the Circle Length Calculator free?
Yes. It is completely free, needs no sign-up, and can be used as many times as you like.
Try our Circle Length Calculator to convert between the radius, diameter and length (circumference) of any circle in seconds.